hamrock, jacobson and schmid©1998 mcgraw-hill chapter 18: flexible machine elements scientists...

Hamrock, Jacobson and Schmid©1998 McGraw-Hill

Chapter 18: Flexible Machine Elements

Scientists study the world as it is, engineers create the world that has never been.Theodore von Karman

Image: An assortment of chains and belts and their associated sprockets and pulleys. Courtesy of Sterling Instrument Co.


Open Flat Belt

Figure 18.1 Dimensions, angles of contact, and center distance of open flat belt.

Text Reference: Figure 18.1, page 828


Weighted Idler

Figure 18.2 Weighted idler used to maintain desired belt tension.



Timing Belt


Figure 18.3 Synchronous, or timing, belt.


V-Belt in Sheave Groove

Figure 18.4 V-belt in sheave groove.



Overload FactorsDriven unit Overload

factorAgitators

LiquidSemiliquid

1.21.4

CompressorCentrifugalReciprocating

1.21.4

Conveyors and elevatorsPackage, ovenBelt

1.21.4

Fans and blowersCentrifugal, calculatingExhausters

1.21.4

Food machinersSlicersGrinders and mixers

1.21.4

GeneratorsFarm lighting and exciters 1.2

Heating and ventilatingFans and oil burnersStokers

1.22.4

Laundry machineryDryers and ironersWashers

1.21.4

Machine toolsHome workshop and woodworking 1.4

PumpsCentrifugalRecprocating

1.21.4

Table 18.1 Overload service factors (f1) for various types of driven unit.

Text Reference: Table 18.1, page 835


Minimum Pulley Pitch Diameter

Table 18.2 Recommended minimum pitch diameters of pulley for three belt sizes.


Belt Size of belt, in. Minimum pitch diameter, in.type Recommended Absolute2L3L4L

1/4 x 1/81/4 x 7/321/2 x 5/16

1.01.52.5

1.01.51.8


Recommended Pulley Diameter


Table 18.3 Recommended pulley diameters in inches for three electric motor sizes.

Motor speed, rpmMotor 575 695 870 1160 1750horsepower, hp Recommended pulley diameter, in.

0.500.751.00

2.503.003.00

2.502.503.00

2.502.502.50

-2.502.50

--

2.25


Arc Correction FactorsLoss in arc ofcontact, deg

Correctionfactor

Loss in arc ofcontact, deg

Correctionfactor

051015202530354045

1.000.990.980.960.950.930.920.890.890.87

505560657075808690

0.860.840.830.810.790.760.740.710.69

Table 18.4 Arc correction factors for various angles of loss in arc of contact.



Power Ratings for Light Duty V-BeltSpeed of faster Pulley effective outside diameter, in.

shaft, rpm 1.00 2.00 3.00 4.00 5.00 6.00Rated horsepower, hp

116017503450500

100015002000250030003500400045005000

0.050.070.140.040.050.060.080.100.120.140.160.180.20

0.080.130.240.050.080.120.150.180.210.240.280.310.35

0.120.200.350.060.120.170.230.270.310.350.380.42

0.160.250.440.080.160.220.280.340.400.440.46

0.190.280.440.100.190.250.320.390.410.44

0.210.34

0.120.210.300.390.440.47

Table 18.5 Power ratings for light duty V-belt. (a) 2L section with wt=1/4 in. and ht=1/8 in.



Power Ratings for Light Duty V-Belt (cont.)

Table 18.5 Power ratings for light duty V-belt. (b) 3L section with wt=3/8 in. and ht=1/4 in.


S peed of Pul ley effective outside diameter, in.

faster shaft, 1.50 1.75 2.00 2.25 2.50 2.75 3.00rpm Rated horsepower, hp116017503450500

100015002000250030003500400045005000

0.070.090.110.040.070.090.100.110.110.110.110.100.09

0.130.170.250.070.120.150.190.210.230.250.260.250.26

0.180.250.380.090.160.220.270.310.350.380.400.420.42

0.230.320.500.120.210.290.350.410.450.500.540.560.57

0.280.390.620.140.250.350.430.510.570.620.660.680.69

0.340.460.730.170.300.410.510.600.680.740.780.800.80

0.390.540.830.190.340.470.590.690.780.840.880.900.89


Power Ratings for Light Duty V-Belt (cont.)

Table 18.5 Power ratings for light duty V-belt. (c) 4L section with wt=1/2 in. and ht=9/32 in.


S peed of Pulley effective outside diameter, in.faster shaft, 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00

rpm Rated horsepower, hp.116017503450500

100015002000250030003500400045005000

0.120.120.020.080.110.120.110.090.060.02

---

0.230.280.300.140.210.260.300.310.310.300.270.220.15

0.340.440.570.190.310.400.470.530.560.570.560.540.47

0.450.600.830.240.410.540.650.730.790.830.830.810.75

0.560.751.070.290.500.670.820.941.021.071.091.071.01

0.670.901.300.340.600.810.991.131.241.311.331.301.23

0.771.0510520.390.690.941.151.321.451.531.551.511.41

0.881.201.730.440.781.071.311.511.651.731.751.691.66

0.981.341.920.490.871.201.471.691.841.921.921.841.65


Center DistancesPulley combination Normal center distance

Driver pitch Driver pitch Short center Medium center

diameter, in. diameter, in. Beltnumber

Centerdistance,

in.

Beltnumber

Centerdistance,

in.2.03.02.02.03.02.02.02.252.53.02.02.03.02.02.02.0.1.5

2.03.02.53.04.53.54.04.55.06.05.06.09.07.09.010.09.0

3L2003L2503L2103L2203L2903L2403L2503L2703L2903L3303L2503L3103L4103L3403L3903L4203L390

6.47.46.66.78.27.37.27.78.18.98.08.610.39.29.910.410.1

3L2503L3103L2703L2803L3503L3003L3103L3303L3503L3903L3403L3703L4703L4003L4503L4803L450

9.410.49.69.711.210.310.310.711.111.911.011.613.412.213.013.613.3

Table 18.6 Center distances for various pitch diameters of driver and driven pulleys. (a) 3L type of V-belt.



Center Distances (cont.)

Table 18.6 Center distances for various pitch diameters of driver and driven pulleys. (b) 4L type of V-belt.


Driver Driver Minimum center Short center Medium centerpitch

diameter,in.

pitchdiameter,

in.Belt

number

Centerdistance,

in.Belt

number

Centerdistance,

in.Belt

number

Centerdistance,

in.2.53.03.04.03.03.53.04.03.03.54.03.04.03.03.52.04.02.42.52.82.02.02.53.02.0

2.53.04.56.06.07.07.5

10.09.0

10.512.010.514.012.014.09.0

18.012.018.014.011.012.015.013.014.0

4L1704L2004L2404L3004L2804L3204L3204L4104L3604L4204L4704L4104L5304L4504L5204L3504L6504L4404L4804L5104L4004L4304L5304L6304L490

4.04.85.56.56.27.06.88.57.58.89.68.6

10.59.1

10.47.5

12.88.99.3

10.38.08.5

10.312.29.5


8.08.89.6

10.610.311.111.012.511.713.013.812.915.013.414.811.817.313.314.314.712.513014.916.814.1


12.012.813.614.514.315.115.016.715.817.118.017.019.117.619.015.921.617.518.519.016.717.319.221.218.4


Wire Rope

Figure 18.5 Cross section of wire rope.



Rope Lay

Figure 18.6 Two lays of wire rope. (a) Lang; (b) regular.



Wire Rope Data

Rope

Weightper

height,lb/f t

Minimum sheavediameter,

in.

Ropediameter,

d, in.Material

Si ze ofouterwires

Modulusof

elasticitya

psiStrengthb

psi

6 x 7 Haulage

6 x 19Standardhoi st ing

6 x 37 Specialfl exibl e

8 x 19 Ext rafl exibl e

7 x 7 Aircraft

7 x 9 Aircraft

19-Wi reaircraft

1 .50d2

1.60d2

1.55d2

1.45d2

1.70d2

1.75d2

2.15d2

42d

26d-34d

18d

21d-26d

-

-

-

1/4 - 1 1/2

1/4 - 2 3/4

1/4 - 3 1/2

1/4 - 1 1/2

1/16 - 3/8

1/8 - 1 3/8

1/32 - 5/16

Monitor s teelP low st eel

Mild plow s teelMonitor s teel

P low st eelMild plow s teelMonitor s teel

P low st eelMonitor s teel

P low st eelCorros ion-

res is tant s teelCarbon s teelCorros ion-

res is tant s teelCarbon s teelCorros ion-

res is tant s teelCarbon s teel

d /9d /9d /9

d /13-d /16d /13-d /16d /13-d /16

d / 22d / 22

d /15-d /19d /15-d /19

-

--

--

-

14 x 106

14 x 106

14 x 106

12 x 106

12 x 106

12 x 106

11 x 106

11 x 106

10 x 106

10 x 106

-

--

--

-

100 x 103

88 x 103

76 x 103

106 x 103

93 x 103

80 x 103

100 x 103

88 x 103

92 x 103

80 x 103

124 x 103

124 x 103

135 x 103

143 x 103

165 x 103

165 x 103

aThe modulus of el as ti city is only approximate; it is affected by the loads on t he rope and, in general , i ncreaseswi th the l ife of the rope.bThe s trength i s based on t he nominal area of t he rope. The figures given are only approximate and are based on 1-in. rope si zes and 1/4 in . ai rcraft cable s izes.

Table 18.7 Wire rope data [From Shigley and Mitchell (1983)]



Minimum Safety Factors for Wire Rope

Application Safety factora, ns

Track cablesGuysMine shafts, ft

Up to 5001000-20002000-3000Over 3000

HoistingHaulageCranes and derricksElectric hoistsHand elevatorsPrivate elevatorsHand dumbwaitersGrain elevatorsPassenger elevators, ft/min

5030080012001500

Freight elevators, ft/min5030080012001500

3.23.5

8.07.06.05.05.06.06.07.05.07.54.57.5

7.609.20

11.2511.8011.90

6.658.20

10.0010.5010.55

Table 18.8 Minimum safety factors for variety of wire rope applications. [from Shigley and Mitchell (1983)]



Loss in Rope Strength vs. D/d Ratio

Figure 18.7 Percent strength loss in wire rope for different D/d ratios.



Service Life vs. D/d ratio

Figure 18.8 Service life for different D/d ratios.



Maximum Allowable Bending Pressures for Wire Rope

MaterialWooda Cast Ironb Cast stee lc Chilled cast

irondManganese

stee le

Rope Allowable be aring pressure, pall, psiRegular Lay

6 x 76 x 196 x 378 x 19

Lang Lay6 x 76 x 196 x 37

150250300350

165275330

300480585680

350550660

550900

10751260

60010001180

650110013251550

71512101450

1470240030003500

165027503300

aOn end grain of beech, hickory or gumbFor HB(min.)=125.c30-40 carbon; HB(min.)=160.dUse only with uniform surface hardness.eFor high sp eeds with balanced sheaves having ground surfaces.

Table 18.9 Maximum allowable bending pressures for various sheave materials and types of rope. [From Shigley and Mitchell (1983)]



Rolling Chain


Figure 18.9 Various parts of a rolling chain.


Strengths of Rolling ChainsRoller Pin Link Average

Chainnumber

PitchPt, in.

Diameterin.

Width,in.

diameter, d, in.

platethickness,

a

ultimatestrength,

Su, lbf

Weightper foot,

lbf25

a

35a

41b

40506080

100120140160180200240

1/43/81/21/25/83/41

1 1/41 1/21 3/4

22 1/42 1/2

3

0.1300.200a

0.3065/162/5

15/325/83/47/81

1 1/81 13/321 9/161 7/8

1/83/161/4

5/163/81/25/83/411

1 1/41 13/32

1 1/21 7/8

0.09050.1410.1410.1560.2000.2340.3120.3750.4370.5000.5620.6870.7810.937

0.0300.0500.0500.0600.0800.0940.1250.1560.1870.2190.2500.2810.3120.375

87521002000370061008500

14500240003400046000580007600095000130000

0.0840.210.280.410.681.001.692.493.674.936.438.7010.5116.90

aWithout ro llersbLightweight rollers


Table 18.10 Standard sizes and strengths of rolling chains.


Chordal Rise


Figure 18.10 Chordal rise in rolling chains.


Transmitted Power

Table 18.11 Transmitted power of single-strand, no. 25 rolling chain.



Rolling Chain Service Factors

Type of input power

Type of drivenload

Internalcombustion engine

with hydraulicdrive

Electric motoror

turbine

Internalcombustionengine withmechanical

driveSmoothModerate shockHeavy shock

1.01.21.4

1.01.31.5

1.21.41.7

Table 18.12 Service factors for rolling chains.



Multiple-strand Factors

Number of strands Multiple-strand factor, a2

234

1.72.53.3

Table 18.13 Multiple strand factors for rolling chains.



Dragline

Figure 18.11 Typical dragline.


hamrock, jacobson and schmid©1998 mcgraw-hill chapter 18: flexible machine elements scientists...

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